Scattering of Polarized Neutrons by Protons

Abstract

IN spite of many attempts, it has not been possible so far to develop a theory of nuclear forces which accounts in a satisfactory way for all the properties of even the simplest system, a neutron and a proton. An alternative procedure might, therefore, be attempted, namely, to obtain the interaction potential empirically from the various observed properties like the binding energy, quadrupole moment, magnetic moment of the deuteron and the scattering cross-section. The latter seems particularly useful for this purpose, as there exist general reciprocal quantum mechanical relations between the differential scattering cross-section dσ and the interaction potential; dσ is expressed in terms of certain phase shifts ŋl, (l = 0, 1, 2, . . .), suffered by the partial waves of different orbital angular momentum l due to the interaction between the two particles. For spinless particles, a knowledge of d (as a function of the angle of scattering θ) determines all the phase shifts ŋl and vice versa, and a knowledge of the phase shift ŋl (as a function of energy) for a given l-state determines the interaction potential for that l-state and vice versa. However, the fact that the neutron–proton system splits into the singlet and triplet states (with different interactions) makes the determination of the phase-shifts from a knowledge of dσ (θ) alone impossible.